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Quantile Regression (QR) can be used to estimate aleatoric uncertainty indeep neural networks and can generate prediction intervals. Quantifyinguncertainty is particularly important in critical applications such as clinicaldiagnosis, where a realistic assessment of uncertainty is essential indetermining disease status and planning the appropriate treatment. The mostcommon application of quantile regression models is in cases where theparametric likelihood cannot be specified. Although quantile regression isquite robust to outlier response observations, it can be sensitive to outliercovariate observations (features). Outlier features can compromise theperformance of deep learning regression problems such as style translation,image reconstruction, and deep anomaly detection, potentially leading tomisleading conclusions. To address this problem, we propose a robust solutionfor quantile regression that incorporates concepts from robust divergence. Wecompare the performance of our proposed method with (i) least trimmed quantileregression and (ii) robust regression based on the regularization ofcase-specific parameters in a simple real dataset in the presence of outlier.These methods have not been applied in a deep learning framework. We alsodemonstrate the applicability of the proposed method by applying it to amedical imaging translation task using diffusion models.

Beta quantile regression for robust estimation of uncertainty in the presence of outliers